milkcloud

You're welcome. However, I will not straight up just give you the answer because I already gave you an explanation on how to solve this problem. This site is meant for learning, not for people to just get an answer then leave. 

I do not quite understand your question, but I'm going to assume you mean: 

Arthur is organising his collection of films. He has 60 all together. The ratio of comedy films to action films to Norris films is 2 : 7 : 1. How many types of each film does he have?

Step 1. Add together 2, 7, and 1. 

Step 2. Divide 60 by the sum you calculated in Step 1.

Step 3. Take the quotient you calculated in Step 2, then mulitply it by 2, 7, and 1, to get the answer to how many comedy films, action films, and Norris films Arthur has, respectively.

To solve this problem, we can first do 8 + 5. 8 + 5 = 13.

Next, divide 1040 by 13. 1040 / 13 = 80. The 80 represents every 'part' of the ratio (in this case the 'parts' are 5 and 8). 

Finally, mulitply 5 * 80, and 8 * 80.

5 * 80 is the amount of money Miss Penny put into her savings, and 8 * 80 is the amount she spent. 

(You still need to simplify those expressions to get the answer)

I hope this helped! If I made a mistake somewhere or you want me to explain more on why I did those steps, please lmk! 

Anytime!

Sure. 

Here are the steps you can take to solve this problem. 

1. Find the average of 1 ice cream cone. (360 divided by 6)

2. Mulitply the avarage by 7, since the problem wants you to find the cost of 7 ice cream cones.

If you follow these two steps, I'm sure you will get the correct answer. If you want me to explain further on why you should do these two steps, I can explain. Good luck!

(Assuming that each ice cream cone costs the same amount of money)

1. Find the average of 1 ice cream cone. (Average: 420 / 6 = 70)

2. Mulitply the avarage by 11, since the problem wants you to find the cost of 11 ice cream cones. ( 70 * 11 = 770 )

Conclusion: 11 ice cream cones cost 770 pence. 

Hope this helped! 

I'm going to assume you mean x / ( x - 5 ) = 4 / ( x - 4 ). 
From that equation, we can cross multiply and get x ( x - 4 ) = 4 ( x - 5 ).

Expand. x^2 - 4x = 4x - 20. 
To make it easier to find all values of x, set the equation equal to zero. x^2 - 8x + 20 = 0. 
Plugging this into the Quadratic Formula, we get x = [ 8 ± sqrt ( 64 - 4 * 1 * 20 ) ] / ( 2 * 1 ). 
Simplify. x = 4 ± 2i. 

(Simplifiying steps: 

1. Simplify the inside of the square root: x = [ 8 ± sqrt ( -16 ) ] / ( 2 * 1 )

2. Simplify the denominator: x = [ 8 ± sqrt ( -16 ) ] / 2

3. Separate the fraction two parts: x = ( 8 / 2 ) ± [ ( sqrt -16 ) / 2 ]

4. Simplify the two fractions: x = 4 ± 2i

    (Basically doing 8 / 2, and solving the imaginary fraction ( ( i * sqrt 16 ) / 2 = 4i / 2 = 2i ) )
 

I hope I helped! A bit rusty on this topic, so if I made any mistake please lmk!